could anyone please help me with the following problem A pic

could anyone please help me with the following problem. A pic of the problem is attached below.

Computer. This question concerns numerically exploring the solutions of the equation P_n+1 = P_n + 0.1p_n(1 -P_n)(2 -p_n) First determine all the equilibrium solutions of this difference equation. Numerically simulate the difference equation using the following initial conditions p_0 = 0 P_0 = 0.0001 P_0 = .9999 p_0 = 1 P_0 = 1.0001 p_0 = 1.9999 P_0 = 2 P_0 = 2.0001 Describe your results and comment on the stability of the equilibrium you found. Provide plots of all your results. It will make your comparisons easier if

Solution

P_n+1 = P_n + 0.1*P_n * (1-P_n)* (2-P_n);

here, original solution is;

P_n =  P_n + 0.1*P_n * (1-P_n)* (2-P_n);

P_n = 0;

P_n = 1;

P_n = 2;

Now, solving on Excel we get;

From solving for Pn we get the following result;

Solution has equilibrium around Pn = 1;

P0	0	0.0001	0.9999	1	1.0001	1.9999	2	2.0001
P1	0	0.0003	1	1	1	1.9997	2	2.0003
P2	0	0.0009	1	1	1	1.9991	2	2.0009
P3	0	0.002696	1	1	1	1.997304	2	2.002704
P4	0	0.008068	1	1	1	1.991932	2	2.008132
P5	0	0.024008	1	1	1	1.975992	2	2.024596
P6	0	0.07031	1	1	1	1.92969	2	2.075619
P7	0	0.196446	1	1	1	1.803554	2	2.244444
P8	0	0.481146	1	1	1	1.518854	2	2.927198
P9	0	0.86032	1	1	1	1.13968	2	8.157792
P10	0	0.997275	1	1	1	1.002725	2	367.7223
P11	0	1	1	1	1	1	2	49318723
P12	0	1	1	1	1	1	2	1.2E+23
P13	0	1	1	1	1	1	2	1.73E+69
P14	0	1	1	1	1	1	2	5.1E+207
P15	0	1	1	1	1	1	2	#NUM!
P16	0	1	1	1	1	1	2	#NUM!